Simulation of bar with a straightness defect crossing a cylindrical guidance tool using the hybrid elerian lagrangian (HEL) formalism

This data set presents the hybrid eulerian-lagrangian (HEL) formalism in finite element modelling. It consists of coupling steady state (eulerian) and time depending (lagrangian) phenomena, that occur in material flow, using Arlequin method. Each type of phenomenon is represented by an appropriate mesh. In this dataset it is exposed how HEL can be useful for long and flat product fabrication. Contact areas with tools have steady state aspect. Outside, structural instabilities inducing geometrical defects are time depending. In this context HEL offers the opportunity to model material drawing in contact with three or two dimensional eulerian elements and structural behavior outside with lagrangian (improved with ALE formalism) shell or beam elements. The animation in the dataset presents a representative two-dimensional case of circular cross-sectional steel bar passing through guidance tool. Inside contact with tool two dimensional mesh with quadrilateral linear elements is used (20x3 elements). Structural behavior (straightness) is characterized by mesh with quadratic beam elements (30 elements). At eulerian mesh extremities, incoming and outgoing velocities (identical and equal to 1000mm/s) are imposed at inlet and outlet of contact area (eulerian mesh) which makes lagrangian mesh transported from upstream to downstream. Contact is supposed frictionless and replaced by blocking vertical velocities in the upper and lower surfaces in the eulerian mesh. Upstream and downstream extremeties of the beam are fixed (vertical velocity and displacement are blocked to stabilize the structure). A case with incoming defect is presented and bar supposed not stretched. Time increment is constant in the simulation and taken 0.5ms.

本数据集介绍了有限元建模中的混合欧拉-拉格朗日（hybrid eulerian-lagrangian, HEL）形式化方法，该方法通过阿尔坎（Arlequin）方法，耦合材料流动中出现的稳态（欧拉）与随时间变化的（拉格朗日）两类现象，每一类现象均采用适配的网格进行表征。本数据集阐述了HEL方法如何应用于长扁材制备：与工具的接触区域呈现稳态特性，而外部引发几何缺陷的结构不稳定性则随时间演化；在此场景下，HEL方法可实现如下建模：采用二维或三维欧拉单元对接触区域的材料拉拔过程进行建模，同时采用经任意拉格朗日-欧拉（Arbitrary Lagrangian-Eulerian, ALE）格式改进的拉格朗日壳单元或梁单元对外部区域的结构行为进行建模。数据集中的动画展示了一个典型的二维案例：圆形截面钢筋通过导向工具的过程，在与工具接触的区域，采用了包含20×3个四边形线性单元的二维网格，表征结构平直度的部分则采用了含30个二次梁单元的网格；在欧拉网格的两端，接触区域（欧拉网格区域）的进出口流速被设定为恒定值1000mm/s，以此驱动拉格朗日网格从上游向下游移动。本次模拟假设接触为无摩擦状态，并通过约束欧拉网格上下表面的垂直速度来等效替代实际接触约束，梁单元的上下游两端被固定（约束垂直速度与位移以稳定结构）；数据集还展示了带有初始缺陷的工况，此时钢筋未受拉伸，模拟中的时间步长恒定为0.5ms。